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Fairness has less impact when agents are less informed

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Abstract

Research from the last four decades suggests that fairness plays an important role in economic transactions. However, the vast majority of this research investigates behavior in an environment where agents are fully informed. We develop a new experimental paradigm—nesting the widely used ultimatum game—and find that fairness has less impact on outcomes when agents are less informed. As we remove information, offers become less generous and unfair offers are more likely to be accepted.

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Notes

  1. Early experimental evidence from the ultimatum game found that subjects deviated from equilibrium predictions based on self-interested agents (Selten, 1978; Roth et al., 1981; Güth et al., 1982).

  2. See early discussions (Binmore et al., 1985; Ochs & Roth, 1989; Prasnikar & Roth, 1992) and more recent ones (Levitt & List, 2007; Carpenter, 2010).

  3. That seminal work explores a setting where the pie is relatively more valuable to one of the two parties (i.e. the tokens that the subjects split are worth 3 times more for one subject than the other), allowing for self-serving definitions of fairness to arise. We explore a simpler setting where the pie being split is equally valuable to both parties.

  4. These results focus on the last 10 rounds of the game, after subjects gain experience. However, results from all 30 rounds show consistent findings.

  5. In related work, Klempt et al. (2019) analyzes the effects of asymmetric information when either the proposer or the responder is better informed in the ultimatum and dictator game. See also Siegel and Fouraker (1960), which explored bilateral bargaining games in a different experimental paradigm but also considered the role of information on outcomes.

  6. Another related literature builds off of the “acquiring-a-company” game (Samuelson & Bazerman, 1984) and explores the impact of information available to buyers and sellers (Güth et al., 2017, 2019). Because that game was designed to explore the winner’s curse, however, it typically involves additional uncertainty for one or both parties, such as parties not knowing their own payoff from transacting.

  7. Three sessions of each treatment were run at Wharton and two sessions of each treatment were run at Stanford. As shown in Appendix Table B6, there were no substantial differences by location and so we pool the data in what follows.

  8. While rare, this type of overly generous offer is more likely to occur when buyers are uninformed of the seller’s cost and so are unlikely to know that they have offered over half of the pie. When the buyer is informed, less than 2.5% of offers are overly generous.

  9. We define two alternative definitions of inequality share that differently handle the small number of cases where buyers are overly generous and offer the seller a larger share of the pie than they keep. These offers can be seen as increasing inequality at the transactional level or reducing inequality at the market level. Absolute Inequality Share \(=\frac{| \pi _B - \pi _S|}{V-C}\) is the absolute difference between the buyer and seller’s earnings divided by the total surplus and treats offers that give the majority of the surplus to the seller as increasing inequality. Difference Inequality Share \(=\frac{ \pi _B - \pi _S}{V-C}\) is the difference in earnings between buyers and sellers divided by the total surplus, which is allowed to be negative and thus treats offers that give the majority of the surplus to the seller as decreasing inequality.

  10. Note that since the surplus available for a given transaction, \(V-C\), differs across rounds, we report all outcomes in terms of the fraction of surplus that was available in a given round.

  11. Appendix Table B1 shows corresponding results for all 30 rounds, the first 10 rounds, and the last 10 rounds (replicating the results in Table 2). The regressions that we use to assess significance in Appendix Table B1 are shown in Appendix Tables B2–B4. We find differences in play between the first 10 and last 10 rounds: across all treatments, Buyer Share, Seller Share, and Total Share increase as subjects play more rounds while Rejection Rate, which is equal to \(1-\)Total Share, falls. We confirm there are significant differences in a regression framework, shown in Appendix Table B5, which compares outcomes in the first 10 rounds and the last 10 rounds.

  12. Appendix Table B6 presents results for participants at Wharton and Stanford separately and shows that differences between participants at the two schools are not statistically significant. Appendix Table B7 shows that results are consistent and significant using session clusters. Appendix Table B8 shows that our results on inequality from Table 2 are robust to using the two alternative measures of inequality.

  13. Appendix Figure B1 summarizes these results and points to where these results are documented.

  14. These differences are consistent and statistically significant when examining all 30 rounds of the game (see Appendix Figure B2 and the left panel of Appendix Table B12).

  15. This is consistent with work by Ockenfels and Werner (2012) in which dictators “hide behind the small cake” when the size of the pie is unknown. While our setting does not have a reputational component because identities are not known, this result may also be consistent with a model of reputation formation (Camerer & Weigelt, 1988; Jung et al., 1994; Embrey et al., 2014).

  16. We used a Becker–DeGroot–Marschak (BDM) method for binary outcomes. To supplement the BDM instructions, we also explicitly emphasized for subjects that the method incentivized honest reporting of beliefs (see instructions in Appendix Section C).

  17. In this section, we focus on buyer beliefs conditional on offers between 20 and 60 experimental units, where most of our data is concentrated. Figure B4 in the appendix presents the cumulative distribution functions of offers used to elicit beliefs and shows that more than 99% of offers are between 20 and 60 experimental units.

  18. The data in panel (c) is slightly noisier, but beliefs in the Neither Knows treatment do not vary much by value and are slightly above acceptance probability beliefs in the Seller Knows treatment when low offers are made.

  19. If each offer corresponded to a certain buyer’s value (i.e., no pooling) then we would not have seen differences by treatment.

  20. See Appendix Table B13 for regression results across all 30 rounds and the last 10 rounds.

  21. Appendix Figure B5 replicates this graph for all 30 rounds and the left panel of Appendix Table B13 shows the corresponding regression results.

  22. We used a Becker–DeGroot–Marschak (BDM) method for binary outcomes. To supplement the BDM instructions, we also explicitly emphasized for subjects that the method incentivized honest reporting of beliefs (see instructions in Appendix Section C).

  23. While not our focus here, exploring cases where information acquisition is private information is an exciting avenue for future work. For example, Roth and Keith Murnighan (1982) shows more disagreement in a lottery game when the information setting itself is not common knowledge.

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Authors and Affiliations

  1. The Wharton School, University of Pennsylvania, Philadelphia, USA

    Jennie Huang

  2. The Wharton School, University of Pennsylvania, Philadelphia, USA

    Judd B. Kessler

  3. Stanford University, Stanford, USA

    Muriel Niederle

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  1. Jennie Huang
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Correspondence to Judd B. Kessler.

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Huang, J., Kessler, J.B. & Niederle, M. Fairness has less impact when agents are less informed. Exp Econ 27, 155–174 (2024). https://doi.org/10.1007/s10683-023-09795-w

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